Question: Jessica is 3 times as old as Omar. Twenty years ago, Jessica was 7 times as old as Omar. How old is Omar now?
Explanation: We can use the given information to write down two equations that describe the ages of Jessica and Omar. Let Jessica's current age be $j$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $j = 3o$ Twenty years ago, Jessica was $j - 20$ years old, and Omar was $o - 20$ years old. The information in the second sentence can be expressed in the following equation: $j - 20 = 7(o - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 3o$ . Substituting this into our second equation, we get: $3o$ $-$ $20 = 7(o - 20)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $3 o - 20 = 7 o - 140$ Solving for $o$ , we get: $4 o = 120.$ $o = 30$.